Question

A rectangle field has a perimeter of 220 meters and an area of 2856 square meters. What are the dimensions?

Answer 1

The dimensions are 68 meters by 42 meters.

Explanation:

Let the length be x

Let the width be y

Perimeter = 220 meter

So,
`2x+2y=220`

or
`x+y=110` or
`x=110-y` ...........(1)

Area = 2856 square meter

So,
`xy=2856` ............(2)

Substituting the value of x from (1) in (2)

`(110-y)y=2856`

=>
`110y-y^(2)=2856`

=>
`y^(2)-110y+2856=0`

Solving this equation, we get roots as y = 68 and y = 42

So, if we put y = 68, we get x = 42

If we put y = 42, we get x = 68

As length is longer than width, we will take length = 68 meters and width = 42 meters.

Hence, the dimensions are 68 meters by 42 meters.